Energy cascade processes in stratified turbulence

The atmospheric energy spectrum as a function of horizontal wavenumber over the range from a few kilometers to the synoptic scales was obtained by Nastrom et al. (1984) and Nastrom and Gage (1985). They found that the spectra follow the −3 power law in the range 1000 to 3000 km and the −5/3 power law in the horizontal scales less than a few hundred km (about 400–500 km). While the −3 power law is interpreted as the property of quasi-geostrophic turbulence (Charney, 1971), the formation mechanism of the −5/3 spectral slope in the atmospheric mesoscales is still uncertain. Lilly (1983) suggested that inverse energy cascade could occur in stratified turbulence. However, Métais et al. (1994) showed that effective upscale energy cascade and a −5/3 spectral slope are not realized for the parameter range of the atmospheric mesoscales. Although Koshyk et al. (1999, 2001) performed the numerical simulation using the GFDL-SKYHI GCM and achieved reproduction of the −3 slope in the synoptic scales and the −5/3 slope in the mesoscales, there is no study using a simple dynamical model which supports and reproduces their results. In order to investigate formation process of the k −5/